中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (4): 115-118.doi: 10.13471/j.cnki.acta.snus.2019.04.012

• 论文 • 上一篇    下一篇

正整数n的分部量不小于2的有序分拆数

唐保祥1,任韩2   

  1. 1.天水师范学院数学与统计学院,甘肃 天水 741001;
    2.华东师范大学数学系,上海 200062
  • 收稿日期:2018-11-30 出版日期:2019-07-25 发布日期:2019-07-25

The number of ordered splits where the components of a positive integer n are not less than 2

TANG Baoxiang1, REN Han2   

  1. 1. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China;
    2. Department of Mathematics, East China Normal University, Shanghai 200062, China  
  • Received:2018-11-30 Online:2019-07-25 Published:2019-07-25

摘要:

首先利用递推方法求出了正整数 n 各分部量不大于2的分拆数的公式;其次建立了正整数 n 各分部量不大于2的有序分拆的集合与正整数  n+2各分部量不小于2的有序分拆集合之间的双射,从而得到了正整数 n+2各分部量不小于2的有序分拆数的公式;最后给出了正整数  n 的各分部量不大于3和4的有序分拆数的递推关系式,以及正整数 n 各分部量是2,或3,或4的有序分拆数的递推关系式。

关键词: 有序分拆, 递推关系式, 双射

Abstract:

Firstly, the formula of the fraction of positive integer n is not more than 2 is obtained by using the recursive method. Secondly, the bijection of the ordered split sets between the fraction of positive integer  n is not more than 2 and the fraction of positive integer  n+2 is not less than 2 is established, so that the formula for calculating the ordered split number of the positive integer  n+2 is not less than 2 is obtained. Finally, when the fraction of positive integer  n is not more than 3 or 4, and is 2, 3 or 4, the recursive relations of the ordered split number are given.

Key words: components, recursive relation, bijection

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